How to Find the Vertex of a Parabola (NancyPi). MIT grad explains how to find the vertex of a parabola. You can get the vertex from the parabola equation (standard form or vertex form). To skip ahead: 1) For how to find the X-COORDINATE of the vertex point from a STANDARD FORM equation of a parabola (like y = -2x^2 + 4x + 1), skip to time 0:16. 2) For how to find the Y-COORDINATE of the vertex, skip to time 1:34. 3) For how to get the vertex point from VERTEX FORM instead [like y = 2(x - 1)^2 + 3], skip to 2:24. 4) For what to do if the signs are confusing (ex. if the equation has X PLUS A NUMBER instead of x minus, like in y = 2(x + 3)^2 + 4), skip to 3:34. Nancy formerly of MathBFF explains the steps.
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HOW TO FIND VERTEX:
How you find the vertex depends on whether the equation you're given is in "standard form" or "vertex form". How do you know if your problem is vertex or standard form? Each one has a very different form.
What is standard form? The STANDARD FORM equation is a quadratic polynomial and looks like y = ax^2 + bx + c without any parentheses (it has not been changed into another form by completing the square). If your equation looks like this, your vertex will be a point with an x-coordinate that is -b/(2a) where you can find a and b by comparing the standard form parabola formula to the equation you were given. Then, you can get the vertex y-coordinate by taking your original equation and plugging in the x-coordinate you found and simplifying until you've solved for y.
The VERTEX FORM is also a quadratic equation but is in the form y = a(x - h)^2 + k. It's easier and faster to find the vertex from the parabola vertex form, because the vertex is just the point (h,k) and h and k are values you can pull straight from the equation by matching the equation you were given with the vertex form formula that uses h and k. If your given quadratic equation has x plus a number, in parentheses, instead of minus a number, like y = 2(x + 3)^2, then you can rewrite the equation as subtraction of a number, like y = 2(x - (-3))^2, since adding 3 is the same as subtracting negative 3. This means that your h value will be negative 3.
Note: if you want to be able to convert your standard form into vertex form with a perfect square in your equation, you will need to "complete the square" first to get your parabola equation into vertex form.
On the graph of a quadratic function or parabola, the vertex is either the lowest point on the parabola (the minimum) if the parabola is opening up, or it is the highest point on the parabola (the maximum) if the parabola is opening down.
For more of my Algebra, Algebra 2, College Algebra, and Geometry math videos on quadratic functions and help with other mathematics topics, check out: http://nancypi.com
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